


def      UpperCAmelCase__		(UpperCamelCase_				,UpperCamelCase_							):



     """simple docstring"""






     snake_case											=							1  # To kept the Calculated Value
     # Since C(n, k) = C(n, n-k)
     if k > (n - k):
          snake_case											=							n - k
     # Calculate C(n,k)
     for i in range(UpperCamelCase_							):
          result *= n - i
          result //= i + 1
     return result
def      UpperCAmelCase__		(UpperCamelCase_							):



     """simple docstring"""






     return binomial_coefficient(2 * node_count				,UpperCamelCase_							) // (node_count + 1)
def      UpperCAmelCase__		(UpperCamelCase_							):



     """simple docstring"""






     if n < 0:
          raise ValueError('''factorial() not defined for negative values'''							)
     snake_case											=							1
     for i in range(1				,n + 1							):
          result *= i
     return result
def      UpperCAmelCase__		(UpperCamelCase_							):



     """simple docstring"""






     return catalan_number(UpperCamelCase_							) * factorial(UpperCamelCase_							)


if __name__ == "__main__":
 _SCREAMING_SNAKE_CASE     :					List[Any]      =       int(input("Enter the number of nodes: ").strip() or 0)
 if node_count <= 0:
  raise ValueError("We need some nodes to work with.")
 print(
     f'''Given {node_count} nodes, there are {binary_tree_count(node_count)} '''
     f'''binary trees and {catalan_number(node_count)} binary search trees.'''
 )








from ..utils import DummyObject, requires_backends

class     A__   (       metaclass=snake_case__      ):







    """simple docstring"""

    __magic_name__         =						['flax', 'transformers']
    def __init__(			self     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(self     ,   ['''flax''', '''transformers''']       )
    @classmethod
    def 						a_     (			cls     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(cls     ,   ['''flax''', '''transformers''']       )




    @classmethod
    def 						a_     (			cls     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(cls     ,   ['''flax''', '''transformers''']       )






class     A__   (       metaclass=snake_case__      ):







    """simple docstring"""

    __magic_name__         =						['flax', 'transformers']
    def __init__(			self     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(self     ,   ['''flax''', '''transformers''']       )
    @classmethod
    def 						a_     (			cls     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(cls     ,   ['''flax''', '''transformers''']       )




    @classmethod
    def 						a_     (			cls     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(cls     ,   ['''flax''', '''transformers''']       )






class     A__   (       metaclass=snake_case__      ):







    """simple docstring"""

    __magic_name__         =						['flax', 'transformers']
    def __init__(			self     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(self     ,   ['''flax''', '''transformers''']       )
    @classmethod
    def 						a_     (			cls     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(cls     ,   ['''flax''', '''transformers''']       )




    @classmethod
    def 						a_     (			cls     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(cls     ,   ['''flax''', '''transformers''']       )






class     A__   (       metaclass=snake_case__      ):







    """simple docstring"""

    __magic_name__         =						['flax', 'transformers']
    def __init__(			self     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(self     ,   ['''flax''', '''transformers''']       )
    @classmethod
    def 						a_     (			cls     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(cls     ,   ['''flax''', '''transformers''']       )




    @classmethod
    def 						a_     (			cls     ,   *__snake_case     ,   **__snake_case       ):
         requires_backends(cls     ,   ['''flax''', '''transformers''']       )




